// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_EULERANGLESCLASS_H // TODO: Fix previous "EIGEN_EULERANGLES_H" definition?
#define EIGEN_EULERANGLESCLASS_H

namespace Eigen {
/** \class EulerAngles
 *
 * \ingroup EulerAngles_Module
 *
 * \brief Represents a rotation in a 3 dimensional space as three Euler angles.
 *
 * Euler rotation is a set of three rotation of three angles over three fixed axes, defined by the EulerSystem given as
 * a template parameter.
 *
 * Here is how intrinsic Euler angles works:
 *  - first, rotate the axes system over the alpha axis in angle alpha
 *  - then, rotate the axes system over the beta axis(which was rotated in the first stage) in angle beta
 *  - then, rotate the axes system over the gamma axis(which was rotated in the two stages above) in angle gamma
 *
 * \note This class support only intrinsic Euler angles for simplicity,
 *  see EulerSystem how to easily overcome this for extrinsic systems.
 *
 * ### Rotation representation and conversions ###
 *
 * It has been proved(see Wikipedia link below) that every rotation can be represented
 *  by Euler angles, but there is no single representation (e.g. unlike rotation matrices).
 * Therefore, you can convert from Eigen rotation and to them
 *  (including rotation matrices, which is not called "rotations" by Eigen design).
 *
 * Euler angles usually used for:
 *  - convenient human representation of rotation, especially in interactive GUI.
 *  - gimbal systems and robotics
 *  - efficient encoding(i.e. 3 floats only) of rotation for network protocols.
 *
 * However, Euler angles are slow comparing to quaternion or matrices,
 *  because their unnatural math definition, although it's simple for human.
 * To overcome this, this class provide easy movement from the math friendly representation
 *  to the human friendly representation, and vise-versa.
 *
 * All the user need to do is a safe simple C++ type conversion,
 *  and this class take care for the math.
 * Additionally, some axes related computation is done in compile time.
 *
 * #### Euler angles ranges in conversions ####
 * Rotations representation as EulerAngles are not single (unlike matrices),
 *  and even have infinite EulerAngles representations.<BR>
 * For example, add or subtract 2*PI from either angle of EulerAngles
 *  and you'll get the same rotation.
 * This is the general reason for infinite representation,
 *  but it's not the only general reason for not having a single representation.
 *
 * When converting rotation to EulerAngles, this class convert it to specific ranges
 * When converting some rotation to EulerAngles, the rules for ranges are as follow:
 * - If the rotation we converting from is an EulerAngles
 *  (even when it represented as RotationBase explicitly), angles ranges are __undefined__.
 * - otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR>
 *   As for Beta angle:
 *    - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2].
 *    - otherwise:
 *      - If the beta axis is positive, the beta angle will be in the range [0, PI]
 *      - If the beta axis is negative, the beta angle will be in the range [-PI, 0]
 *
 * \sa EulerAngles(const MatrixBase<Derived>&)
 * \sa EulerAngles(const RotationBase<Derived, 3>&)
 *
 * ### Convenient user typedefs ###
 *
 * Convenient typedefs for EulerAngles exist for float and double scalar,
 *  in a form of EulerAngles{A}{B}{C}{scalar},
 *  e.g. \ref EulerAnglesXYZd, \ref EulerAnglesZYZf.
 *
 * Only for positive axes{+x,+y,+z} Euler systems are have convenient typedef.
 * If you need negative axes{-x,-y,-z}, it is recommended to create you own typedef with
 *  a word that represent what you need.
 *
 * ### Example ###
 *
 * \include EulerAngles.cpp
 * Output: \verbinclude EulerAngles.out
 *
 * ### Additional reading ###
 *
 * If you're want to get more idea about how Euler system work in Eigen see EulerSystem.
 *
 * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles
 *
 * \tparam _Scalar the scalar type, i.e. the type of the angles.
 *
 * \tparam _System the EulerSystem to use, which represents the axes of rotation.
 */
template<typename _Scalar, class _System>
class EulerAngles : public RotationBase<EulerAngles<_Scalar, _System>, 3>
{
  public:
	typedef RotationBase<EulerAngles<_Scalar, _System>, 3> Base;

	/** the scalar type of the angles */
	typedef _Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;

	/** the EulerSystem to use, which represents the axes of rotation. */
	typedef _System System;

	typedef Matrix<Scalar, 3, 3> Matrix3;	   /*!< the equivalent rotation matrix type */
	typedef Matrix<Scalar, 3, 1> Vector3;	   /*!< the equivalent 3 dimension vector type */
	typedef Quaternion<Scalar> QuaternionType; /*!< the equivalent quaternion type */
	typedef AngleAxis<Scalar> AngleAxisType;   /*!< the equivalent angle-axis type */

	/** \returns the axis vector of the first (alpha) rotation */
	static Vector3 AlphaAxisVector()
	{
		const Vector3& u = Vector3::Unit(System::AlphaAxisAbs - 1);
		return System::IsAlphaOpposite ? -u : u;
	}

	/** \returns the axis vector of the second (beta) rotation */
	static Vector3 BetaAxisVector()
	{
		const Vector3& u = Vector3::Unit(System::BetaAxisAbs - 1);
		return System::IsBetaOpposite ? -u : u;
	}

	/** \returns the axis vector of the third (gamma) rotation */
	static Vector3 GammaAxisVector()
	{
		const Vector3& u = Vector3::Unit(System::GammaAxisAbs - 1);
		return System::IsGammaOpposite ? -u : u;
	}

  private:
	Vector3 m_angles;

  public:
	/** Default constructor without initialization. */
	EulerAngles() {}
	/** Constructs and initialize an EulerAngles (\p alpha, \p beta, \p gamma). */
	EulerAngles(const Scalar& alpha, const Scalar& beta, const Scalar& gamma)
		: m_angles(alpha, beta, gamma)
	{
	}

	// TODO: Test this constructor
	/** Constructs and initialize an EulerAngles from the array data {alpha, beta, gamma} */
	explicit EulerAngles(const Scalar* data)
		: m_angles(data)
	{
	}

	/** Constructs and initializes an EulerAngles from either:
	 *  - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1),
	 *  - a 3D vector expression representing Euler angles.
	 *
	 * \note If \p other is a 3x3 rotation matrix, the angles range rules will be as follow:<BR>
	 *  Alpha and gamma angles will be in the range [-PI, PI].<BR>
	 *  As for Beta angle:
	 *   - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2].
	 *   - otherwise:
	 *     - If the beta axis is positive, the beta angle will be in the range [0, PI]
	 *     - If the beta axis is negative, the beta angle will be in the range [-PI, 0]
	 */
	template<typename Derived>
	explicit EulerAngles(const MatrixBase<Derived>& other)
	{
		*this = other;
	}

	/** Constructs and initialize Euler angles from a rotation \p rot.
	 *
	 * \note If \p rot is an EulerAngles (even when it represented as RotationBase explicitly),
	 *  angles ranges are __undefined__.
	 *  Otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR>
	 *  As for Beta angle:
	 *   - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2].
	 *   - otherwise:
	 *     - If the beta axis is positive, the beta angle will be in the range [0, PI]
	 *     - If the beta axis is negative, the beta angle will be in the range [-PI, 0]
	 */
	template<typename Derived>
	EulerAngles(const RotationBase<Derived, 3>& rot)
	{
		System::CalcEulerAngles(*this, rot.toRotationMatrix());
	}

	/*EulerAngles(const QuaternionType& q)
	{
	  // TODO: Implement it in a faster way for quaternions
	  // According to http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/
	  //  we can compute only the needed matrix cells and then convert to euler angles. (see ZYX example below)
	  // Currently we compute all matrix cells from quaternion.

	  // Special case only for ZYX
	  //Scalar y2 = q.y() * q.y();
	  //m_angles[0] = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z())));
	  //m_angles[1] = std::asin( 2*(q.w()*q.y() - q.z()*q.x()));
	  //m_angles[2] = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2)));
	}*/

	/** \returns The angle values stored in a vector (alpha, beta, gamma). */
	const Vector3& angles() const { return m_angles; }
	/** \returns A read-write reference to the angle values stored in a vector (alpha, beta, gamma). */
	Vector3& angles() { return m_angles; }

	/** \returns The value of the first angle. */
	Scalar alpha() const { return m_angles[0]; }
	/** \returns A read-write reference to the angle of the first angle. */
	Scalar& alpha() { return m_angles[0]; }

	/** \returns The value of the second angle. */
	Scalar beta() const { return m_angles[1]; }
	/** \returns A read-write reference to the angle of the second angle. */
	Scalar& beta() { return m_angles[1]; }

	/** \returns The value of the third angle. */
	Scalar gamma() const { return m_angles[2]; }
	/** \returns A read-write reference to the angle of the third angle. */
	Scalar& gamma() { return m_angles[2]; }

	/** \returns The Euler angles rotation inverse (which is as same as the negative),
	 *  (-alpha, -beta, -gamma).
	 */
	EulerAngles inverse() const
	{
		EulerAngles res;
		res.m_angles = -m_angles;
		return res;
	}

	/** \returns The Euler angles rotation negative (which is as same as the inverse),
	 *  (-alpha, -beta, -gamma).
	 */
	EulerAngles operator-() const { return inverse(); }

	/** Set \c *this from either:
	 *  - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1),
	 *  - a 3D vector expression representing Euler angles.
	 *
	 * See EulerAngles(const MatrixBase<Derived, 3>&) for more information about
	 *  angles ranges output.
	 */
	template<class Derived>
	EulerAngles& operator=(const MatrixBase<Derived>& other)
	{
		EIGEN_STATIC_ASSERT(
			(internal::is_same<Scalar, typename Derived::Scalar>::value),
			YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)

		internal::eulerangles_assign_impl<System, Derived>::run(*this, other.derived());
		return *this;
	}

	// TODO: Assign and construct from another EulerAngles (with different system)

	/** Set \c *this from a rotation.
	 *
	 * See EulerAngles(const RotationBase<Derived, 3>&) for more information about
	 *  angles ranges output.
	 */
	template<typename Derived>
	EulerAngles& operator=(const RotationBase<Derived, 3>& rot)
	{
		System::CalcEulerAngles(*this, rot.toRotationMatrix());
		return *this;
	}

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	 * determined by \a prec.
	 *
	 * \sa MatrixBase::isApprox() */
	bool isApprox(const EulerAngles& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
	{
		return angles().isApprox(other.angles(), prec);
	}

	/** \returns an equivalent 3x3 rotation matrix. */
	Matrix3 toRotationMatrix() const
	{
		// TODO: Calc it faster
		return static_cast<QuaternionType>(*this).toRotationMatrix();
	}

	/** Convert the Euler angles to quaternion. */
	operator QuaternionType() const
	{
		return AngleAxisType(alpha(), AlphaAxisVector()) * AngleAxisType(beta(), BetaAxisVector()) *
			   AngleAxisType(gamma(), GammaAxisVector());
	}

	friend std::ostream& operator<<(std::ostream& s, const EulerAngles<Scalar, System>& eulerAngles)
	{
		s << eulerAngles.angles().transpose();
		return s;
	}

	/** \returns \c *this with scalar type casted to \a NewScalarType */
	template<typename NewScalarType>
	EulerAngles<NewScalarType, System> cast() const
	{
		EulerAngles<NewScalarType, System> e;
		e.angles() = angles().template cast<NewScalarType>();
		return e;
	}
};

#define EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(AXES, SCALAR_TYPE, SCALAR_POSTFIX)                                           \
	/** \ingroup EulerAngles_Module */                                                                                 \
	typedef EulerAngles<SCALAR_TYPE, EulerSystem##AXES> EulerAngles##AXES##SCALAR_POSTFIX;

#define EIGEN_EULER_ANGLES_TYPEDEFS(SCALAR_TYPE, SCALAR_POSTFIX)                                                       \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYZ, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYX, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZY, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZX, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
                                                                                                                       \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZX, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZY, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXZ, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXY, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
                                                                                                                       \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXY, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXZ, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYX, SCALAR_TYPE, SCALAR_POSTFIX)                                                \
	EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYZ, SCALAR_TYPE, SCALAR_POSTFIX)

EIGEN_EULER_ANGLES_TYPEDEFS(float, f)
EIGEN_EULER_ANGLES_TYPEDEFS(double, d)

namespace internal {
template<typename _Scalar, class _System>
struct traits<EulerAngles<_Scalar, _System>>
{
	typedef _Scalar Scalar;
};

// set from a rotation matrix
template<class System, class Other>
struct eulerangles_assign_impl<System, Other, 3, 3>
{
	typedef typename Other::Scalar Scalar;
	static void run(EulerAngles<Scalar, System>& e, const Other& m) { System::CalcEulerAngles(e, m); }
};

// set from a vector of Euler angles
template<class System, class Other>
struct eulerangles_assign_impl<System, Other, 3, 1>
{
	typedef typename Other::Scalar Scalar;
	static void run(EulerAngles<Scalar, System>& e, const Other& vec) { e.angles() = vec; }
};
}
}

#endif // EIGEN_EULERANGLESCLASS_H
